4.121 Albinism. People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms (called alleles), which we denote by a and A. Each person has a pair of these genes, one inherited from each parent. A child inherits one of each parent’s two alleles independently with probability 0.5. Albinism is a recessive trait, so a person is albino only if the inherited pair is aa.
(a) Beth’s parents are not albino but she has an albino brother. This implies that both of Beth’s parents have type Aa. Why?
(b) Which of the types aa, Aa, AA could a child of Beth’s parents have? What is the probability of each type?
(c) Beth is not albino. What are the conditional probabilities for Beth’s possible genetic types, given this fact? (Use the definition of conditional probability.)